I was so excited to find this thread! I'm attending WashU in the Fall (PhD in Applied Psych of Learning & Motivation in Dept of Ed), but I've lived in STL since ~2013, and I love to share information about the city. I lived in the downtown STL area for several years, then moved to Clayton 2 years ago. My husband also attended WashU (JD, MBA), so our lives have always revolved around the campus, which we lived 5 minutes from by car. I'm happy to answer any questions about life here, but I don't explore the city as much as I used to when living downtown; Clayton is fairly sleepy, as is most of the county, and we're usually too lazy to drive back into the city to do things.
For housing, I'd recommend sharing a house near WashU or looking at the new developments in the Delmar Loop. The high-rise buildings in Clayton are great and have lots of studios and 1BRs, but the price is a bit higher. I have a car, but plan on using the Metro to get to campus, which is only feasible if you find housing along its route (St. Louis is anything but walkable, so having a car is great, and traffic isn't an issue).
Any first-timers should visit Forest Park (Boathouse, Amphitheatre, etc.), the Arch, the Central West End, the Zoo, the Botanical Gardens, the Cardinals Stadium, the Blues Stadium, the almost-finished Soccer Stadium, and the Ferris Wheel. For food, the best offerings are generally BBQ (Pappy's and Sugarfire are my personal faves), but there are lots of stand-outs (Lona's Lil Eats, Seedz Cafe, Guerrilla Street Food, The Dam, Pi Pizzeria, Lulu's, Natasha's, Rooster, Bailey's Range, Hi-Pointe Drive-In) that can usually be found in Tower Grove or Central West End. The food is reasonably-priced and the portions are sizeable.